It is shown that the integral functional
I
(
y
,
z
)
=
∫
G
f
(
t
,
y
(
t
)
,
z
(
t
)
)
d
μ
I(y,z) = {\smallint _G}f(t,y(t),z(t))d\mu
is lower semicontinuous on its domain with respect to the joint strong convergence of
y
k
→
y
{y_k} \to y
in
L
p
(
G
)
{L_p}(G)
and the weak convergence of
z
k
→
z
{z_k} \to z
in
L
p
(
G
)
{L_p}(G)
, where
1
≤
p
≤
∞
1 \leq p \leq \infty
and
1
≤
q
≤
∞
1 \leq q \leq \infty
, under the following conditions. The function
f
:
(
t
,
x
,
w
)
→
f
(
t
,
x
,
w
)
f:(t,x,w) \to f(t,x,w)
is measurable in t for fixed (x, w), is continuous in (x, w) for a.e. t, and is convex in w for fixed (t, x).